/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 43 A beam of partially polarized li... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 34: Problem 43

A beam of partially polarized light can be considered to be a mixture of polarized and unpolarized light. Suppose we send such a beam through a polarizing filter and then rotate the filter through \(360^{\circ}\) while keeping it perpendicular to the beam. If the transmitted intensity varies by a factor of \(5.0\) during the rotation, what fraction of the intensity of the original beam is associated with the beam's polarized light?

Short Answer

Expert verified
0.8

Step by step solution

01

Understand the problem

We need to find the fraction of the intensity of the original beam that is associated with the polarized light. The transmitted intensity varies by a factor of 5.0 as the polarizing filter is rotated 360 degrees.
02

Define Variables

Let the intensity of the unpolarized light component be denoted as \(I_{up}\) and the intensity of the polarized light component be denoted as \(I_p\). The maximum transmitted intensity (when the filter is aligned with the polarization direction) is \(I_{max} = I_{up} + I_p\). The minimum transmitted intensity (when the filter is orthogonal to the polarization direction) is \(I_{min} = I_{up}\).
03

Set up the Intensity Ratio

Given that the intensity varies by a factor of 5, we have \(\frac{I_{max}}{I_{min}} = 5.0\). Thus, \(\frac{I_{up} + I_p}{I_{up}} = 5.0\).
04

Simplify the Equation

Simplify the equation: \(\frac{I_{up} + I_p}{I_{up}} = 5.0 \Rightarrow I_{up} + I_p = 5 I_{up} \Rightarrow I_p = 4 I_{up}\).
05

Calculate the Fraction

The total original intensity \(I_0\) is \( I_0 = I_{up} + I_p \Rightarrow I_0 = I_{up} + 4 I_{up} = 5 I_{up}\). The fraction of the intensity associated with the polarized light is therefore: \( \frac{I_p}{I_0} = \frac{4 I_{up}}{5 I_{up}} = \frac{4}{5} = 0.8 \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Polarization
Polarization refers to the orientation of the oscillations in a transverse wave, particularly in electromagnetic waves like light. Most natural light sources, such as the sun or a bulb, emit unpolarized light, meaning the waves vibrate in multiple planes. However, when a wave is polarized, its oscillations are limited to a single plane. Polarized light can be achieved through reflection, refraction, or by passing the light through a polarizing filter.
Intensity Variation
In the context of light and polarizing filters, intensity variation describes how the brightness of a light beam changes as it passes through a polarizing filter. When the transmission axis of the polarizing filter is aligned with the direction of polarization of the light, the intensity is at its maximum. Conversely, when the transmission axis is perpendicular to the direction of polarization, the intensity is at its minimum. The factor by which the intensity varies gives us valuable information about the nature of the light, such as the degree of polarization.
Polarizing Filter
A polarizing filter is a device used to produce polarized light from unpolarized light. It works by allowing waves of a certain orientation to pass through while blocking others. Polarizing filters are commonly used in photography to reduce glare and in scientific instruments to control and analyze light. When a beam of partially polarized light passes through a rotating polarizing filter, the intensity of the transmitted light varies, which is a key principle used to determine the properties of the light.
Unpolarized Light
Unpolarized light consists of waves that vibrate in multiple planes perpendicular to the direction of propagation. Common sources of light, like the sun or artificial lights, typically emit unpolarized light. When unpolarized light passes through a polarizing filter, only the component of the light vibrating in the direction of the filter's transmission axis passes through, resulting in polarized light. Unpolarized light is an essential concept to understand when analyzing light behavior with polarizing filters.
Light Beam Analysis
Analyzing a light beam involves understanding its properties, including its intensity and polarization state. In the given exercise, you analyze the light by observing how its intensity varies as it passes through a polarizing filter. The variation in intensity during the rotation of the filter helps you determine the fraction of the light that is polarized. Using equations that relate the maximum and minimum transmitted intensities to the amount of polarized and unpolarized light, you can break down the complex behavior of light into understandable components. This analysis is powerful for both academic studies and practical applications in fields like optics and photonics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Some neodymium-glass lasers can provide 100 terawatts of power in \(1.0 \mathrm{~ns}\) pulses at a wavelength of \(0.26 \mu \mathrm{m}\). How much energy is contained in a single pulse?

(A) How long does it take a radio signal to travel \(150 \mathrm{~km}\) from a transmitter to a receiving antenna? (b) We see a full Moon by reflected sunlight. How much earlier did the light that enters our eye leave the Sun? The Earth-Moon and Earth-Sun distances are \(3.8 \times 10^{5} \mathrm{~km}\) and \(1.5 \times 10^{8}\) \(\mathrm{km}\). (c) What is the round-trip travel time for light between the Earth and a spaceship or- biting Saturn, \(1.3 \times 10^{9} \mathrm{~km}\) distant? (d) The Crab nebula, which is about 6500 light-years (ly) distant, is thought to be the result of a supernova explosion recorded by Chinese astronomers in A.D. 1054 . In approximately what year did the explosion actually occur?

A plane electromagnetic wave has a maximum electric field of \(3.20 \times 10^{-4} \mathrm{~V} / \mathrm{m}\). Find the maximum magnetic field.

A particle in the solar system in under the combined influence of the Sun's gravitational attraction and the radiation force due to the Sun's rays. Assume that the particle is a sphere of density \(1.0 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\) and that all the incident light is absorbed. (a) Show that, if its radius is less than some critical radius \(R\), the particle will be blown out of the solar system. (b) Calculate the critical radius.

A beam of unpolarized light is sent through two polarizing sheets placed one on top of the other. What must be the angle between the polarizing directions of the sheets if the intensity of the transmitted light is to be one-third the incident intensity?
See all solutions

Recommended explanations on Physics Textbooks

Scientific Method Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Electric Charge Field and Potential

Read Explanation

Wave Optics

Read Explanation

Medical Physics

Read Explanation

Linear Momentum

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.